New one cycle criteria for optimizing preventive replacement policies

• The Single cycle age replacement model is extended incorporating repairable failures.
• In order to avoid project interruption costs, three model variants are discussed.
• Model variants are replace first, replace last and replace next.
• In many cases analytic solutions are derived and illustrated by numerical examples.
• The different model variants and their results are compared based on simulation studies.

Models are introduced and examined for the optimum scheduling of preventive replacements. The “replace first” and “replace last” models are known from the literature if the long term expected cost per unit time is minimized. We will first introduce the one cycle counterparts of these models when the expected costs per unit time in a single cycle is minimized. If the unit performs identical projects sequentially then the “replace next” model assumes that the preventive replacement is postponed until the ongoing project is finished. The termination time of this project is random which also depends on the scheduled time of the preventive replacement in contrary to the “replace first” and “replace last” models. The mathematical models are formulated and conditions are given for the existence of finite optima. Numerical examples and a simulation study illustrate the methodology and the numerical results show interesting comparisons of the different models.